Multilevel Path Branching for Digital Options

TL;DR

This paper introduces a novel Monte Carlo estimator for digital options that uses path splitting and correlation techniques, achieving efficiency comparable to MLMC for Lipschitz payoffs.

Contribution

It presents a new estimator combining path splitting with MLMC, improving computational efficiency for digital options modeled by SDEs.

Findings

Estimator reduces computational complexity

Effective for digital options with SDE models

Combines path splitting with MLMC for improved performance

Abstract

We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. Combining this new estimator with Multilevel Monte Carlo (MLMC) leads to an estimator with a computational complexity that is similar to the complexity of a MLMC estimator when applied to options with Lipschitz payoffs. This preprint includes detailed calculations and proofs (in grey colour) which are not peer-reviewed and not included in the published article.